# Lesson 2

Representing Proportional Relationships

### Problem 1

The tortoise and the hare are having a race. After the hare runs 16 miles the tortoise has only run 4 miles.

The relationship between the distance $$x$$ the tortoise “runs” in miles for every $$y$$ miles the hare runs is $$y=4x$$. Graph this relationship.

### Problem 2

The table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched.

1. Complete the table.
2. Describe the scales you could use on the $$x$$ and $$y$$ axes of a coordinate grid that would show all the distances and weights in the table.
distance (cm) weight (newtons)
20 28
55
140
1

### Problem 3

Students are selling raffle tickets for a school fundraiser. They collect \$24 for every 10 raffle tickets they sell.

1. Suppose $$M$$ is the amount of money the students collect for selling $$R$$ raffle tickets. Write an equation that reflects the relationship between $$M$$ and $$R$$.
2. Label and scale the axes and graph this situation with $$M$$ on the vertical axis and $$R$$ on the horizontal axis. Make sure the scale is large enough to see how much they would raise if they sell 1000 tickets. 